Dynamics of Solitary Waves Through Taper-Thin Elastic Tube with Localized Deformation

Abstract

In order to elucidate the dynamical behaviour of nonlinear waves in tapered-thin and elastic tubes with localized deformations, we have developed a mathematical model based on equations of inviscid fluid flow in a slowly tapered cone tube. Numerical simulation of the resulting perturbed Korteveg–de Vries equation shows that the amplitude of the velocity wave decreases along the tube as the results of the decrease of the radius and the increase of the rigidity; we also find that the velocity of the pulse velocity wave increases. In the localized deformation area, after some fluctuations, the wave suffers important variations consisting firstly (in the case of constriction) by a decrease and then by an increase. The severity and the length of the variation depend respectively on the amplitude and the gradient scale of the localized deformation. Some biological implications are given.